Benjamin Klusemann

Abstract:

The modeling approach adopted here for nanocrystalline materials is based on the phase-mixture model introduced by Kim, Estrin & Bush (2000). In this model, different deformation mechanisms are assumed to operate in the grain interior and the grain boundaries in parallel. The deformation mechanism in the grain boundaries is associated with the diffusional mass transport along the boundaries, while in the grain interior dislocation glide mechanism as well as diffusion mechanisms are considered. The model is capable of correctly predicting the transition of the flow stress from the Hall-Petch behavior in the conventional grain size range to an inverse Hall-Petch relation for nanocrystalline materials. The original model showed an increase of the strain rate sensitivity with decreasing grain size. However, this type of behavior is only observed in face-centered cubic (fcc) materials. By contrast, nanocrystalline body-centered cubic (bcc) materials show a decrease of the strain rate sensitivity with decreasing grain size. To account for experimental observations for bcc materials, we have modified the original phase-mixture model in the nanocrystalline regime. We assume that plastic deformation in bcc materials is governed by the Peierls mechanism, while the constraints put on the dislocation kink formation by the small grain size are considered to be responsible for a decrease of the strain rate sensitivity with grain refinement. The model for dislocation glide is modified accordingly. Additionally, we look into the effect of strain gradients on the mechanical response of nanocrystalline materials. The phase mixture model is augmented with gradient terms of higher order, namely second and fourth order. Differences in the mechanical behavior of fcc and bcc nanocrystalline materials are discussed in terms of the numerical results obtained with this gradient enhanced model. Details and challenges of the numerical implementation of higher order gradient terms will be provided.